Roll out pastry; fit into a 9 ½ inch deep dish pie pan; sculpt edge into an upstanding ridge; place in freezer for 15 minutes, then partially prebake (tear off about 16 inches foil; tuck the foil into the pie shell, let the excess foil on the ends just flare out like wings; pour in enough dried beans to reach the top of the pan; preheat oven to 400°; bake pie shell on center oven rack for 15 minutes; slowly lift out foil with beans; prick pastry all over the bottom with a fork) and let cool.
Decrease oven temperature to 350°.
Melt butter in a small, preferably nonstick saucepan over very low heat.
Chop the chocolate; add it to the saucepan when the butter is almost melted.
When the butter is completely melted, turn off the heat but leave pan in place for another minute or so, tilting and swirling it once or twice so the hot butter runs over the chocolate.
Remove pan from the heat; wait 3-4 minutes, then whisk the chocolate until smooth.
Set aside to cool.
Add walnuts to a food processor with ¼ cup sugar, the cocoa, flour, and salt; pulse repeatedly until the nuts are very finely chopped; set aside.
Using an electric mixer, beat the eggs and remaining ¾ cup sugar in a big mixing bowl until quite light and airy, about 4 minutes.
Add in Kahlua, vanilla, and nut mixture; beat again until smooth.
Add in chocolate mixture and beat briefly until the filling is uniformly mixed; pour filling into the cooled pie shell.
Place pie on the center oven rack and bake for 35 minutes; expect the pie to puff up and don’t be surprised if the top develops a crack or two; also expect the filling to seem relatively loose under the crusted.
Transfer pie to a wire rack; let cool thoroughly; the pie can be sliced once it has cooled, but the texture will be better for slicing if you refrigerate it for at least 1 hour.